On the invariant representation of spin tensors with applications

The invariant representation of the spin tensor defined as the rotation rate of a principal triad for a symmetric and non-degenerate tensor is derived on the basis of the general solution of a linear tensorial equation. The result can be naturally specified to study the. spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics. A remarkable formula which relates the generalized stress conjugate to the generalized strain in Hill's sense. to Cauchy stress, is obtained in invariant form through the work conjugate principle. Particularly, a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes of strain arc not fixed during deformation.

Model of sources: a proposal for the hierarchy, merging strategy and representation of the information sources in virtual models of historical buildings

Contributed to: Fusion of Cultures: XXXVIII Annual Conference on Computer Applications and Quantitative Methods in Archaeology – CAA2010 (Granada, Spain, Apr 6-9, 2010)

Ontologies for representation of folk song metadata

The digital management of collections in museums, archives, libraries and galleries is an increasingly important part of cultural heritage studies. This paper describes a representation for folk song metadata, based on the Web Ontology Language (OWL) implementation of the CIDOC Conceptual Reference Model. The OWL representation facilitates encoding and reasoning over a genre ontology, while the CIDOC model enables a representation of complex spatial containment and proximity relations among geographic regions. It is shown how complex queries of folk song metadata, relying on inference and not only retrieval, can be expressed in OWL and solved using a description logic reasoner.

A bioregional classification of the continental shelf of northeastern North America for conservation analysis and planning based on representation

Understanding how well National Marine Sanctuaries and other marine protected areas represent the diversity of species present within and among the biogeographic regions where they occur is essential for assessing their conservation value and identifying gaps in the protection of biological diversity. One of the first steps in any such assessment should be the development of clearly defined and scientifically justified planning boundaries representing distinct oceanographic conditions and faunal assemblages. Here, we propose a set of boundaries for the continental shelf of northeastern North America defined by subdivisions of the Eastern Temperate Province, based on a review and synthesis (i.e. meta-analysis) of the scientific literature. According to this review, the Eastern Temperate Province is generally divided into the Acadian and Virginian Subprovinces. Broad agreement places the Scotian Shelf, Gulf of Maine, and Bay of Fundy within the Acadian Subprovince. The proper association of Georges Bank is less clear; some investigators consider it part of the Acadian and others part of the Virginian. Disparate perspectives emerge from the analysis of different groups of organisms. Further, while some studies suggest a distinction between the Southern New England shelf and the rest of the Mid-Atlantic Bight, others describe the region as a broad transition zone with no unique characteristics of its own. We suggest there exists sufficient evidence to consider the Scotian Shelf, Gulf of Maine, Georges Bank, Southern New England, and Southern Mid-Atlantic Bight as distinct biogeographic regions from a conservation planning perspective, and present a set of proposed mapped boundaries. (PDF contains 23 pages.)

Developing alternatives for optimal representation of seafloor habitats and associated communities in Stellwagen Bank National Marine Sanctuary

The implementation of various types of marine protected areas is one of several management tools available for conserving representative examples of the biological diversity within marine ecosystems in general and National Marine Sanctuaries in particular. However, deciding where and how many sites to establish within a given area is frequently hampered by incomplete knowledge of the distribution of organisms and an understanding of the potential tradeoffs that would allow planners to address frequently competing interests in an objective manner. Fortunately, this is beginning to change. Recent studies on the continental shelf of the northeastern United States suggest that substrate and water mass characteristics are highly correlated with the composition of benthic communities and may therefore, serve as proxies for the distribution of biological biodiversity. A detailed geo-referenced interpretative map of major sediment types within Stellwagen Bank National Marine Sanctuary (SBNMS) has recently been developed, and computer-aided decision support tools have reached new levels of sophistication. We demonstrate the use of simulated annealing, a type of mathematical optimization, to identify suites of potential conservation sites within SBNMS that equally represent 1) all major sediment types and 2) derived habitat types based on both sediment and depth in the smallest amount of space. The Sanctuary was divided into 3610 0.5 min2 sampling units. Simulations incorporated constraints on the physical dispersion of sampling units to varying degrees such that solutions included between one and four site clusters. Target representation goals were set at 5, 10, 15, 20, and 25 percent of each sediment type, and 10 and 20 percent of each habitat type. Simulations consisted of 100 runs, from which we identified the best solution (i.e., smallest total area) and four nearoptimal alternates. We also plotted total instances in which each sampling unit occurred in solution sets of the 100 runs as a means of gauging the variety of spatial configurations available under each scenario. Results suggested that the total combined area needed to represent each of the sediment types in equal proportions was equal to the percent representation level sought. Slightly larger areas were required to represent all habitat types at the same representation levels. Total boundary length increased in direct proportion to the number of sites at all levels of representation for simulations involving sediment and habitat classes, but increased more rapidly with number of sites at higher representation levels. There were a large number of alternate spatial configurations at all representation levels, although generally fewer among one and two versus three- and four-site solutions. These differences were less pronounced among simulations targeting habitat representation, suggesting that a similar degree of flexibility is inherent in the spatial arrangement of potential protected area systems containing one versus several sites for similar levels of habitat representation. We attribute these results to the distribution of sediment and depth zones within the Sanctuary, and to the fact that even levels of representation were sought in each scenario. (PDF contains 33 pages.)

An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

23 p. -- An extended abstract of this work appears in the proceedings of the 2012 ACM/IEEE Symposium on Logic in Computer Science